Young massive clusters are dense aggregates of young stars that form the fundamental building blocks of galaxies. Several examples exist in the Milky Way Galaxy and the Local Group, but they are particularly abundant in starburst and interacting galaxies. The few young massive clusters that are close enough to resolve are of prime interest for studying the stellar mass function and the ecological interplay between stellar evolution and stellar dynamics. The distant unresolved clusters may be effectively used to study the star-cluster mass function, and they provide excellent constraints on the formation mechanisms of young cluster populations. Young massive clusters are expected to be the nurseries for many unusual objects, including a wide range of exotic stars and binaries. So far only a few such objects have been found in young massive clusters, although their older cousins, the globular clusters, are unusually rich in stellar exotica. In this review we focus on star clusters younger than ~100 Myr, more than a few current crossing times old, and more massive than ~104 M(sun), irrespective of cluster size or environment. We describe the global properties of the currently known young massive star clusters in the Local Group and beyond, and discuss the state of the art in observations and dynamical modeling of these systems. In order to make this review readable by observers, theorists, and computational astrophysicists, we also review the cross-disciplinary terminology.